The Conservative candidate Angus Macpherson has been elected the first police and crime commissioner (PCC) for Wiltshire on a turnout of just 15.8%, amid predictions from an elections expert that the poll across 41 police areas in England and Wales could yield "the worst turnout for any nationwide set of elections ever".

Green made his comments as Macpherson, a magistrate, became the first commissioner to be elected after winning by 35,319 votes, ahead of Labour's Clare Moody on 21,157. While overall turnout in the county was 15.8%, it was as low as 10.95% in Trowbridge and 10.41% in Devizes, according to unofficial counting.

Professor John Curtice, professor of politics at the University of Strathclyde, said: "It looks pretty likely that certainly we're going below 20%, that this will be the worst turnout for any nationwide set of election ever, and therefore will raise questions, I think, about whether this whole exercise was worth it in the first place.

"The fundamental question is this: who is against the police, and who is in favour of crime? In other words, what really are the significant choices one could put before the electorate about how the job of police and crime commissioner should be done. And, unless there are clear choices to put before the electorate, it is very difficult to persuade voters that [it is worth voting]."

Wiltshire council confirmed that 2,683 ballot papers in the county's race were spoilt – just over 3% of the votes cast – in an election fought under the supplementary vote system.

Curtice told the BBC Radio 4 Today programme that while the two-vote system tended to result in more invalid votes than the first-past-the-post system, the level of spoilt papers "does raise eyebrows".

"It raises this question whether some people didn't simply fail to cast a vote because they were confused by the system, but maybe some people amongst that miniscule 15.8% who turned out actually went to the polling station and then said: 'Hang on, let's spoil that ballot paper to declare we don't think the whole thing is a terribly good idea'."

The Electoral Reform Society had predicted a turnout of 18.5%, which would be below the previous record low for a national poll in peacetime of 23% in the 1999 European parliament elections. But Curtice said the overall figure could be even lower.

One polling station, in Newport in Gwent, received no votes at all. While in Greater Manchester, turnout was just 13.5%, even though a byelection for Manchester Central – retained by Labour – was held the same day. The turnout in Humberside, where Lord Prescott's candidacy raised the profile of the election, was 19.48%, East Riding of Yorkshire council confirmed. The turnout of 19.58% in the Avon and Somerset police election was boosted by a 22.93% turnout in Bristol's first direct election for mayor.

Macpherson told BBC Breakfast that people didn't vote because "they didn't understand what the job is, they didn't know who the candidates were and couldn't make a judgment".

Asked whether the low turnout undermined his mandate, Macpherson told Today: "Of all those that voted, more liked my skill-set than the others'. I think it is not so much a mandate, it is a large job interview. Of course it would be much better if more people had gone out to vote. It is incumbent on all the PCCs, as we take office, to develop this job and let people know what it is."

Voter apathy was also evident in two of three parliamentary byelection results announced.

In other election results to emerge so far:

•Lucy Powell held Manchester Central for Labour with 11,507 votes on a turnout of 18.16%, below the previous record low for a parliamentary byelection of 19.9% in Leeds Central in 1999. The Conservative candidate Matthew Sephton lost his deposit after securing just 754 votes, less than 5% of the total turnout. The swing away from the Liberal Democrats was 16.77%.

• Stephen Doughty retained Labour's Cardiff South and Penarth parliamentary seat after winning almost half of the votes cast on a turnout of 25.65%, with a swing from the Conservatives to Labour of 8.41%.

• The BBC reported that turnout in the Corby byelection, triggered by the decision of Tory MP Louise Mensch to quit to spend more time with her family, was far higher, with 35,733 votes cast – just under 45%. The result is expected at around lunchtime on Friday and will be anxiously awaited by David Cameron and Ed Miliband.

• While Bristol was waiting the result of its first mayoral election, voters in Hartlepool backed the scrapping of the elected mayoral system there. The independent mayor, Stuart Drummond, has held the post since it was established in 2002 and will see out his third term, which ends in May. The electorate backed a switch to a council committee system on a turnout of 18% in a referendum triggered by a motion tabled by the Labour group over the summer.

The bulk of the election results in the 41 constabulary areas outside London will emerge on Friday afternoon.

The shadow home secretary, Yvette Cooper, said the elections for the new commissioners had descended into a shambles, with many voters taking to Twitter to describe the low turnout at their polling stations.

She blamed the lack of information made available about the elections, which will install the first wave of elected individuals to control police budgets, set priorities and have the power to hire and fire chief constables.

Cooper said: "We warned the government repeatedly that they had the wrong approach and that turnout would be low. Theresa May and David Cameron didn't listen and it is shocking that they have spent £100m on these elections rather than on 3,000 police constables instead.

"Time and again on the doorstep people told us either they didn't have enough information, didn't know the elections were happening, didn't support them or didn't want to go out in the dark to vote."